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Question
Your aim is to construct an angle ∠ YPX = 30∘ using a compass and a straight edge only. What is the total number of arcs (not necessarily equal in length) to be drawn to construct an angle of 30∘ after drawing the base ray PX?
Your aim is to construct an angle ∠ YPX = 30∘ using a compass and a straight edge only. What is the total number of arcs (not necessarily equal in length) to be drawn to construct an angle of 30∘ after drawing the base ray PX?
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Solution
The correct option is B 4 arcs
Steps of construction:
1. Draw a ray PX.
2. With P as the centre and any radius, draw an arc, which cuts PX at A. This is the first arc.
3. With A as the centre and the same radius, cut this arc at B. This would be the second arc.
4. With B as the centre and any radius more than half of AB, draw another arc as shown. This is the third arc.
5. With A as the centre and the same radius as above, cut the previously drawn arc at Y. This would the fourth arc.
6. Join P. We have our construction.
4 arcs
Steps of construction:
1. Draw a ray PX.
2. With P as the centre and any radius, draw an arc, which cuts PX at A. This is the first arc.
3. With A as the centre and the same radius, cut this arc at B. This would be the second arc.
4. With B as the centre and any radius more than half of AB, draw another arc as shown. This is the third arc.
5. With A as the centre and the same radius as above, cut the previously drawn arc at Y. This would the fourth arc.
6. Join P. We have our construction.
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